(sin theta-cos theta+1)/(sin theta+cos theta-1)=(1+sin theta)/(cos theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

If ((1+sin theta-cos theta))/((1+sin theta+cos theta))+((1+sin theta+cos theta))/((1+sin theta-cos theta))=4 , then which of the following values will be suitable for theta ? यदि ((1+sin theta-cos theta))/((1+sin theta+cos theta))+((1+sin theta+cos theta))/((1+sin theta-cos theta))=4 है, तो theta के लिए निम्नलिखित में से कौन सा मान उपयुक्त होगा?

(sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta)= ________

(sin theta-cos theta)/(sin theta+cos theta)+(sin theta+cos theta)/(sin theta-cos theta)=(2)/((2sin^(2)theta-1))

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

(cos theta + sin theta )/( cos theta - sin theta )-(cos theta - sin theta )/( cos theta + sin theta ) =

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)).

(sin theta-cos theta + 1) / (sin theta + cos theta-1) = (1) / (sec theta-tan theta)